Type-Ia supernova rates and the progenitor problem, a review

The identity of the progenitor systems of type-Ia supernovae (SNe Ia) is a major unsolved problem in astrophysics. SN Ia rates are providing some striking clues. We review the basics of SN rate measurement, preach about some sins of SN rate measurement and analysis, and illustrate one of these sins with an analogy about Martian scientists. We review the recent progress in measuring SN Ia rates in various environments and redshifts, and their use to reconstruct the SN Ia delay time distribution (DTD) -- the SN rate versus time that would follow a hypothetical brief burst of star formation. A good number of DTD measurements, using a variety of methods, appear to be converging. At delays 1<t<10 Gyr, these measurements show a similar, ~t^-1, power-law shape. The DTD peaks at the shortest delays probed, although there is still some uncertainty regarding its precise shape at t<1 Gyr. At face value, this result supports the idea of a double-degenerate progenitor origin for SNe Ia. Single-degenerate progenitors may still play a role in producing short-delay SNe Ia, or perhaps all SNe Ia, if the red-giant donor channel is more efficient than found by most theoretical models. Apart from the DTD shape, the DTD normalization enjoys fairly good agreement (though perhaps some tension), among the various measurements, with a Hubble-time-integrated DTD value of about 2+/- 1 SNe Ia per 1000 Msun (stellar mass formed with a low-mass-turnover IMF). A recent attempt to characterize the local white dwarf binary population suggests that the white dwarf merger rate can explain the Galactic SN Ia rate, if sub-Chandra mergers lead to SN Ia events. We conclude by pointing to some future directions that should lead to progress in the field, including measurement of the bivariate (delay and stretch) SN Ia response function .